Three well-known combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that the "forgotten symmetric functions" adhere to the complete, the monomial, and the power sums. Also, Carlitz-Riordan Identities (with tables for Second-order Eulerian and Second-order Stirling numbers), Gessel and Stanley multiset permutations (GS-Permutations), Golliwog Numbers (featuring tables and a formula for the numbers called "differences of reciprocal powers of unity"), Pez story problem, and Completion of a Sequence of Carlitz.